Greener Journal of Science, Engineering and Technological Research Vol. 9(1), pp. 3-5, 2019 ISSN: 2276-7835 Copyright ©2019, the copyright of this article is retained by the author(s) http://gjournals.org/GJSETR

Some even expressed as 1+1 or 1-2, 1-4, 1-c, 1+2 can also be expressed as 1-3

Zhou Mi 1*, Honwei Shi 2, Delong Zhang 3, Xingyi Jiang 3, Songting He 3

1 Suqian Economy and Trade Vocational School

2 Suqian College, Industrial technology research institute of Suqian college Jiangsu, Email: 19744090@ qq.com

3 Suqian College

 ABSTRACT According to known conclusions, even numbers can be expressed as 1+2, 1+5, 3+2, 1+c. So this paper derives conclusions partial even expressed as 1+1 or 1-2, 1-4, 1-c, 1+2 can also be expressed as 1-3. ARTICLE INFO Article No.: 040919066 Type: Review Article DOI: 10.15580/GJSETR.2019.1.040919066 Submitted: 09/04/2019 Accepted:  15/04/2019 Published: 19/04/2019 *Corresponding Author Zhou Mi E-mail: zhoumi19920626@ 163.com Keywords: Number theory, a+b, Goldbach conjecture.   Classification code: 0156

INTRODUCTION

Goldbach’s conjecture is that an even number can be represented as a prime number plus a prime number, called “1+1”, According to the theory of Chinese mathematician ChenJing run, a large even number can be expressed as one prime number plus no more than two primes product, It is called “1+ 2”;There is also Wang Yuan’s theory: 1. Large even Numbers can be expressed as the product of two prime Numbers plus three primes product It is called: 3+2; 2.A large even number can be expressed as a prime number plus no more than four prime’s product, it is called 1 plus 4;There is also pan cheng dong’s theory that large even Numbers can be represented as a prime plus 5 prime’s product, called “1+5”.

Based on these known conclusions, this paper concludes that some even Numbers that can be expressed as 1+1 can also be expressed as 1-2, 1-4, 1-c, and some even Numbers that can be expressed as 1+2 can also be expressed as 1-3

Theorem 1.1

Chinese mathematician ChenJing run got : a large even number can be expressed as one prime number plus no more than two primes product, It is called “1+ 2”

Lemma 1.2

Partial even numbers can expressed as 1+1 can also be expressed as 1-2.

Certification

All with p subscripts indicate prime numbers

It is known that 1+2 can indicate all large even numbers proposed by Chen Jingrun,

2N1-p1=p2p3 2N1=p1+p2p3 1+2

There is an even number as the difference between two prime numbers,

2N2+p4=p5 ( 2N2=p5-p4 1-1)

Because of 2N1 representing all large even numbers, N2 included in N1 exist, when they are the same. So

2N1+p4-2N1-p1= p4+p1=p5-p2p3

P4+p1 is 1+1, P5-p2p3 is 1-2, they are equal,

So there are partial even numbers that can be expressed as 1+1 can also be expressed as 1-2.

Theorem 2.1

There is also Wang Yuan’s theory: 1. Large even Numbers can be expressed as the product of two prime Numbers plus three primes product It is called: 3+2;

Lemma 2.2

The presence of an even number that is expressed as 1+2 can also be expressed as 1-3.

Certification

It is known that 3+2 can represent all large even numbers, proposed by Wang Yuan.

2N1-p1p2=p3p4p5 (2N1=p1p2+p3p4p5 2+3)

There is an even number as the difference between two prime numbers

2N2+p6=p7 2N2=p7p6 11

Because of 2N1 representing all large even numbers, N2 included in N1 exist, when they are the same. So 2N1+p6-2N1-p1p2= p6+p1p2 = p7-p3p4p5

P6+p1p2 is 1+2, P7-p3p4p5 is 1-3

So there is the existence that 1+2 can also be expressed as 1-3.

Theorem 3.1

Wang Yuan’s conclusion: A large even number can be expressed as a prime number plus no more than four prime’s product, it is called 1 plus 4.

Lemma 3.2

The presence of a partial even number that is expressed as 1+1 can also be expressed as 1-4.

Certification

Wang Yuan also proved 1+4, the same reason: 1+1 can also be expressed as 1-4.

Theorem 4.1

There is also pan cheng dong’s theory that large even Numbers can be represented as a prime plus 5 prime’s product, called “1+5”.

Lemma 4.2

The presence of a partial even number that is expressed as 1+1 can also be expressed as 1-5.

Certification

It is known that 3+2 can represent all large even numbers, proposed by Pan Chengdong.

2N1-p1=p2p3p4p5p6 2N1=p2p3p4p5p6+p1 1+5

Exist 1-1 2N2+p7=p8 (2N2=p8-p7 1-1)

Because of 2N1 representing all large even numbers, N2 included in N1 exist, when they are the same. So 2N1+p7-2N1-p1=p7+p1=p8-p2p3p4p5p6

P1+p7 is 1+1, P8-p2p3p4p5p6 is 1-5

So there is the existence that 1+1 can also be expressed as 1-5.

Theorem 5.1

Large even numbers can be expressed as 1+cc is a big number.

Lemma 5.2

The presence of a partial even number that is expressed as 1+1 can also be expressed as 1-c.

Certification

Goldbach guessed that “a+b” was completed: 1+c, c is a large natural number. According to the above method, there is the existence that1+1 can also be expressed as 1-c.

ACKNOWLEDGEMENT

I am grateful to the researcher Ge Liming of the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences for listening to my paper. I am grateful to have completed this paper with his encouragement!

REFERENCES

1. Wangyuan, baidubaike, https://baike.baidu.com/item/%E7%8E%8B%E5%85%83/17475?fr=Aladdin

2. panchendong, baidubaike, https://baike.baidu.com/item/%E6%BD%98%E6%89%BF%E6%B4%9E/3712120?fr=aladdin

3. chenjingrun, baidubaike, https://baike.baidu.com/item/%E9%99%88%E6%99%AF%E6%B6%A6/18067?fr=Aladdin

4. gedebahecaix, baidubaik, https://baike.baidu.com/item/%E5%93%A5%E5%BE%B7%E5%B7%B4%E8%B5%AB%E7%8C%9C%E6%83%B3/72364?fr=aladdin

 Cite this Article: Zhou M; Honwei S; Delong Z; Xingyi J; Songting H (2019). Some even expressed as 1+1 or 1-2,1-4, 1-c, 1+2 can also be expressed as 1-3. Greener Journal of Science, Engineering and Technological Research, 9(1): 3-5, http://doi.org/10.15580/GJSETR.2019.1.040919066.